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In 1943, Hadwiger conjectured that every k-chromatic graph has a K_k-minor. While the cases k = 5 and k = 6 have been shown to be equivalent to the
A temporal graph G is a sequence of graphs G1, G2, ... , Gt on the same vertex set. In this talk, we are interested in the analogue of the Travelling
In order to further develop the theory of packing trees and packing forests in an undirected graph, we extended the notion of supermodular functions
In the first paper of the Graph Minors series [JCTB ’83], Robertson and Seymour proved the Forest Minor theorem: the H-minor-free graphs have bounded
Hadwiger's conjecture, first formulated in 1943, is a vast generalization of the four-color theorem, and remains one of the central open problems in
The celebrated Linear Arboricity Conjecture of Akiyama, Exoo, and Harary from 1980 asserts that the edges of every graph with maximum degree Δ can be
A triangulation of a surface is k-irreducible if every edge belongs to a non-contractible curve of length k and there are no shorter non-contractible
We will look at an analogue theorem of the classical Erdős-Pósa Theorem. We prove a $GF(q)$-representable matroid analogue of Robertson and Seymour's
A landmark result of Alon and Shapira characterises testable graph properties by showing that every such property can be described via the Szemerédi
Strong flip-flatness has emerged as a natural dense analogue of uniform almost-wideness in the context of preservation theorems, but its combinatorial